Prediction of radial gas profiles in vertical pipe flow on basis of the bubble size distribution

A method for the prediction of the radial gas profile for a given bubble size distribution is presented. It is based on the assumption of the equilibrium of the forces acting on a bubble perpendicularly to the flow direction. These forces strongly depend on the bubble size. For the simulation of transient flow regime effects, the modelling of several bubble classes in an 1D model and consideration of their radial profiles seems to be more promising than a detailed 3D modelling.
The radial profile of the liquid velocity is calculated by the model of Sato. On the basis of this velocity profile, radial distributions are calculated separately for all bubble classes according to the given bubble size distribution. The sum of these distributions is the radial profile of the gas fraction. It is used in an iteration process to calculate a new velocity profile. There is a strong interaction between the profiles of liquid velocity and gas volume fraction. The model is the basis of a fast running one-dimensional steady state computer code. The results are compared with experimental data obtained for a number of gas and liquid volume flow rates. There is a good agreement between experimental and calculated data. In particular the change from wall peaking to centre peaking gas fraction distribution is well predicted.